Accurate numerical derivatives in MATLAB. Complex step differentiation (CSD) is a technique for computing very accurate numerical derivatives in languages that support complex arithmetic. We describe here the development of a CSD package in MATLAB called PMAD. We have extended work done in other languages for scalars to the arrays that are fundamental to MATLAB. This extension raises questions that we have been able to resolve in a satisfactory way. Our goal has been to make it as easy as possible to compute approximate Jacobians in MATLAB that are all but exact. Although PMAD has a fast option for the expert that implements CSD as in previous work, the default is an object-oriented implementation that asks very little of the user.

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 11 articles )

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  1. Oliver, J.M.; Whiteley, J.P.; Saxton, M.A.; Vella, D.; Zubkov, V.S.; King, J.R.: On contact-line dynamics with mass transfer (2015)
  2. Fateman, Richard: Algorithm differentiation in Lisp: ADIL (2014)
  3. Grégoire-Lacoste, François; Jacquemet, Vincent; Vinet, Alain: Bifurcations, sustained oscillations and torus bursting involving ionic concentrations dynamics in a canine atrial cell model (2014)
  4. Jimenez, J.C.; Sotolongo, A.; Sanchez-Bornot, J.M.: Locally linearized Runge Kutta method of Dormand and Prince (2014)
  5. Patterson, Michael A.; Weinstein, Matthew; Rao, Anil V.: An efficient overloaded method for computing derivatives of mathematical functions in MATLAB (2013)
  6. Taroni, Michele; Vella, Dominic: Multiple equilibria in a simple elastocapillary system (2012)
  7. Al-Mohy, Awad H.; Higham, Nicholas J.: The complex step approximation to the Fréchet derivative of a matrix function (2010)
  8. Avitabile, Daniele; Bridges, Thomas J.: Numerical implementation of complex orthogonalization, parallel transport on Stiefel bundles, and analyticity (2010)
  9. von Bremen, Hubertus F.: Implementation of approach to compute the Lyapunov characteristic exponents for continuous dynamical systems to higher dimensions (2010)
  10. Baker, R.E.; Gaffney, E.A.; Maini, P.K.: Partial differential equations for self-organization in cellular and developmental biology (2008)
  11. Shampine, Lawrence F.: Accurate numerical derivatives in MATLAB. (2007)